Question

3. In ∆ABC, AC = BC. angelBAC is bisected by AD
and AD = AB. Find angleACB.​

Answer 1

Step-by-step explanation:

In triangle ABC, AC = BC

that gives us angle(BAC) = angle (ABC) = A

In triangle ABD, AD = AB

that give us angle (ABD) = angle(ADB)

also angle (ABD) = angle (ABC) = A = angle (ADB) - from above relations.

In triangle ABD,

angle(ABD) = angle (ADB) = A and angle (BAD) = A/2, since AD is angular bisector.

Sum of angles = 180

A + A + A/2 = 180

A = 72.

In triangle ABC, angle (ABC) = angle (BAC) = A and angle (BCA) = C

A + A + C = 180

C = 180 - 2(72) = 36.

C = 36 degrees.